2,094 research outputs found
Information Transmission using the Nonlinear Fourier Transform, Part I: Mathematical Tools
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and
exactly solvable models, is a method for solving integrable partial
differential equations governing wave propagation in certain nonlinear media.
The NFT decorrelates signal degrees-of-freedom in such models, in much the same
way that the Fourier transform does for linear systems. In this three-part
series of papers, this observation is exploited for data transmission over
integrable channels such as optical fibers, where pulse propagation is governed
by the nonlinear Schr\"odinger equation. In this transmission scheme, which can
be viewed as a nonlinear analogue of orthogonal frequency-division multiplexing
commonly used in linear channels, information is encoded in the nonlinear
frequencies and their spectral amplitudes. Unlike most other fiber-optic
transmission schemes, this technique deals with both dispersion and
nonlinearity directly and unconditionally without the need for dispersion or
nonlinearity compensation methods. This first paper explains the mathematical
tools that underlie the method.Comment: This version contains minor updates of IEEE Transactions on
Information Theory, vol. 60, no. 7, pp. 4312--4328, July 201
Information Transmission using the Nonlinear Fourier Transform, Part III: Spectrum Modulation
Motivated by the looming "capacity crunch" in fiber-optic networks,
information transmission over such systems is revisited. Among numerous
distortions, inter-channel interference in multiuser wavelength-division
multiplexing (WDM) is identified as the seemingly intractable factor limiting
the achievable rate at high launch power. However, this distortion and similar
ones arising from nonlinearity are primarily due to the use of methods suited
for linear systems, namely WDM and linear pulse-train transmission, for the
nonlinear optical channel. Exploiting the integrability of the nonlinear
Schr\"odinger (NLS) equation, a nonlinear frequency-division multiplexing
(NFDM) scheme is presented, which directly modulates non-interacting signal
degrees-of-freedom under NLS propagation. The main distinction between this and
previous methods is that NFDM is able to cope with the nonlinearity, and thus,
as the the signal power or transmission distance is increased, the new method
does not suffer from the deterministic cross-talk between signal components
which has degraded the performance of previous approaches. In this paper,
emphasis is placed on modulation of the discrete component of the nonlinear
Fourier transform of the signal and some simple examples of achievable spectral
efficiencies are provided.Comment: Updated version of IEEE Transactions on Information Theory, vol. 60,
no. 7, pp. 4346--4369, July, 201
Information Transmission using the Nonlinear Fourier Transform, Part II: Numerical Methods
In this paper, numerical methods are suggested to compute the discrete and
the continuous spectrum of a signal with respect to the Zakharov-Shabat system,
a Lax operator underlying numerous integrable communication channels including
the nonlinear Schr\"odinger channel, modeling pulse propagation in optical
fibers. These methods are subsequently tested and their ability to estimate the
spectrum are compared against each other. These methods are used to compute the
spectrum of various signals commonly used in the optical fiber communications.
It is found that the layer-peeling and the spectral methods are suitable
schemes to estimate the nonlinear spectra with good accuracy. To illustrate the
structure of the spectrum, the locus of the eigenvalues is determined under
amplitude and phase modulation in a number of examples. It is observed that in
some cases, as signal parameters vary, eigenvalues collide and change their
course of motion. The real axis is typically the place from which new
eigenvalues originate or are absorbed into after traveling a trajectory in the
complex plane.Comment: Minor updates to IEEE Transactions on Information Theory, vol. 60,
no. 7, pp. 4329--4345, July 201
Dual polarization nonlinear Fourier transform-based optical communication system
New services and applications are causing an exponential increase in internet
traffic. In a few years, current fiber optic communication system
infrastructure will not be able to meet this demand because fiber nonlinearity
dramatically limits the information transmission rate. Eigenvalue communication
could potentially overcome these limitations. It relies on a mathematical
technique called "nonlinear Fourier transform (NFT)" to exploit the "hidden"
linearity of the nonlinear Schr\"odinger equation as the master model for
signal propagation in an optical fiber. We present here the theoretical tools
describing the NFT for the Manakov system and report on experimental
transmission results for dual polarization in fiber optic eigenvalue
communications. A transmission of up to 373.5 km with bit error rate less than
the hard-decision forward error correction threshold has been achieved. Our
results demonstrate that dual-polarization NFT can work in practice and enable
an increased spectral efficiency in NFT-based communication systems, which are
currently based on single polarization channels
Capacity-achieving techniques in nonlinear channels
Many of the current optical transmission techniques were developed for linear communication channels and are constrained by the fibre nonlinearity. This paper discusses the potential for radically different approaches to signal transmission and processing based on using inherently nonlinear techniques
Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments
The data recorded in optical fiber [1] and in hydrodynamic [2] experiments
reported the pioneering observation of nonlinear waves with spatiotemporal
localization similar to the Peregrine soliton are examined by using nonlinear
spectral analysis. Our approach is based on the integrable nature of the
one-dimensional focusing nonlinear Schrodinger equation (1D-NLSE) that governs
at leading order the propagation of the optical and hydrodynamic waves in the
two experiments. Nonlinear spectral analysis provides certain spectral
portraits of the analyzed structures that are composed of bands lying in the
complex plane. The spectral portraits can be interpreted within the framework
of the so-called finite gap theory (or periodic inverse scattering transform).
In particular, the number N of bands composing the nonlinear spectrum
determines the genus g = N - 1 of the solution that can be viewed as a measure
of complexity of the space-time evolution of the considered solution. Within
this setting the ideal, rational Peregrine soliton represents a special,
degenerate genus 2 solution. While the fitting procedures employed in [1] and
[2] show that the experimentally observed structures are quite well
approximated by the Peregrine solitons, nonlinear spectral analysis of the
breathers observed both in the optical fiber and in the water tank experiments
reveals that they exhibit spectral portraits associated with more general,
genus 4 finite-gap NLSE solutions. Moreover, the nonlinear spectral analysis
shows that the nonlinear spectrum of the breathers observed in the experiments
slowly changes with the propagation distance, thus confirming the influence of
unavoidable perturbative higher order effects or dissipation in the
experiments
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